from manim import *



class math1(MovingCameraScene):
    def construct(self):
        self.camera.background_color = BLACK  # 设置背景颜色
        self.camera.frame_width = 100  # 设置边框宽度
        self.camera.frame_height = 60  # 设置边框高度
        self.camera.pixel_height = 1080  # 设置像素高度
        self.camera.pixel_width = 1920  # 设置像素宽度
        self.camera.center = ORIGIN  # 设置中心点位置
        self.camera.scale_factor = 1.0  # 设置缩放因子
        #设置横线
        for i in range(60*2+1):       
            dot1=Dot([-500,5*(i-60),0]).set_opacity(0.5)
            dot2=Dot([500,5*(i-60),0]).set_opacity(0.5)
            if i==6:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
                
            else:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
               
            self.add(dot1,dot2,line1)
        #设置竖线
        for i in range(100*2+1):        
            dot3=Dot([(i-100)*5,-300,0]).set_opacity(0.5)
            dot4=Dot([(i-100)*5,300,0]).set_opacity(0.5)
            if i==10:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
                
            else:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
            self.add(dot3,dot4,line2)
        #设置三个点
        dot1 = Dot(radius=1, color=RED)  
        dot1.move_to([-47.5,27.5,0]) 
        dot2 = Dot(radius=1, color=YELLOW)  
        dot2.move_to([-42.5,27.5,0])  
        dot3 = Dot(radius=1, color=GREEN)  
        dot3.move_to([-37.5,27.5,0])
        #镜头跟进效果 
        self.camera.frame.save_state()
        #题目出现
        self.play(self.camera.frame.animate.scale(1.2).move_to([0,-10,0]))
        text = Tex(r"\text{设}$du=\left( axy+y^{2}+3\right) dx+\left( x^{2}+bxy-12\right) dy$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,20,0])
        text0 = Tex(r"\text{且}$u\left( x,y\right) $\text{二阶偏导连续}$,u\left( 0,0\right) =2$\text{求}$u\left( x,y\right) $"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text,RIGHT)
        text1 = Tex(r"\text{解:}$\dfrac{\partial u}{\partial x}=axy+y^{2}+3,\dfrac{\partial u}{\partial y}=x^{2}+bxy-12$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,10,0])
        text2 = Tex(r"\text{由:}$\dfrac{\partial ^{2}u}{\partial x\partial y}=\dfrac{\partial ^{2}u}{\partial y\partial x}\Rightarrow ax+2y=2x+by\Rightarrow a=b=2$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,0,0])
        text3 = Tex(r"$\Rightarrow \dfrac{\partial u}{\partial x}=2xy+y^{2}+3\Rightarrow u\left( x,y\right) =\int \dfrac{\partial u}{\partial x}dx=x^{2}y+xy^{2}+3x+g\left( y\right) $",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,-10,0])
        text4 = Tex(r"$\Rightarrow \dfrac{\partial u}{\partial y}=x^{2}+2xy+g'\left( y\right) \Rightarrow g'\left( y\right) =-12$",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,-20,0])
        text5 = Tex(r"$\Rightarrow g\left( y\right) =-12y+c\Rightarrow u\left( x,y\right) =x^{2}y+xy^{2}+3x-12y+c$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,-30,0])
        text6 = Tex(r"\text{而:}$u\left( 0,0\right) =2\Rightarrow c=2\Rightarrow u\left( x,y\right) =x^{2}y+xy^{2}+3x-12y+2$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,-40,0])





        
        self.play(Create(text),Create(text0),Create(text1),Create(text2),Create(text3),Create(text4),Create(text5),Create(text6))
        #镜头拉回
          #分析文本
        #text100=MarkupText("<b><i>分析/解：</i></b>",color=PINK).scale(5.0).move_to([-38,12.5,0])
        self.play(FadeIn(dot1),run_time=0.1)
        self.play(FadeIn(dot2),run_time=0.1)
        self.play(FadeIn(dot3),run_time=0.1)
        #题目向上移动
       
        self.wait()